Question

You go to a bank and are given these quotes: You can buy a euro for 14 pesos. The bank will pay you 13 pesos for a euro. You can buy a U.S. dollar for .9 euros. The bank will pay you .8 Euros for a U.S. dollar. You can buy a U.S. dollar for 10 pesos. The bank will pay you 9 pesos for a U.S. dollar. You have $1,000. Can you use triangular arbitrage to generate a profit? If so, explain the order of the transactions that you would execute, and the profit that you would earn. If you can not earn a profit from triangular arbitrage, explain why.

Answer 1

First let us put the given data in a tabular format. The bid and ask quotes are from the bank's perspective, bid mean bank buys the base currency in exchange of price currency and ask means the bank sells the base currency for price currency.

Currency Pair	Explanation	Bid	Ask
MXP/EUR	MXP = Mexican Peso EUR = Euro Eur 1 can be bought from the bank for 14 Pesos and sold to the bank for 13 Pesos	13	14
EUR/USD	USD= US Dollar EUR = Euro USD 1 can be bought from the bank for EUR 0.90 and sold to the bank for EUR 0.80	0.80	0.90
MXP/USD	MXP = Mexican Peso USD= US Dollar USD 1 can be bought from the bank for MXP 10 and sold to the bank for MXP 10	9	10

Now to gain triangular arbitrage we can follow the following steps:

• Sell $ 1000 for EUR (Bank buys USD, so we look at the bid rate of EUR/USD quote)
  • EUR 0.80 = $1
  • So $1000= EUR 1000 X 0.80 = 800
• Sell EUR for MXP (Bank buys EUR, so we look at the bid rate of MXP/EUR quote)
  • 1 EUR = MXP 13
  • So EUR 800 = 800x 13= MXP 10400
• Sell MXP for USD (Bank SELLS USD , so we look at the ASK rate of MXP/USD quote)
  • MXP 1 = USD 10
  • So MXP 10400 =10400/10= USD 1040
• So we started with 1000 and ended up with 1040 which is a profit of USD 40
• As more and more people start gaining from it, the demand for MXP and EUR will increase, driving up their rates in terms of other currencies and that would lead to elimination of such profit.